I've tried to see if I give good advice or not, and as it's generally the case things are way simpler in theory
You can find the project I've made in the .zip file, I've added many comments so (I hope) you can get a clear idea of how this work.
LAZER.zip (4.4 MB)
The idea stay the same, do one lazer animation then do some loop , and finally use a transform node to put them in place.
I've used some time offset nodes , I thought they can be animated but in fact it's not possible, so in the end there are many of them.
You'll see that finally for a "simple" effect we quickly go into a little nodal mess, and that technique may be not very straightforward for a beginner . It can be simpler but you'll have to make much more animation. In the other hand doing this more procedurally also takes time, but that's maybe more suited to be reused or modified.
Finally the lazers are not perfectly synchronized with the guns , but I think it still work !
For this effect it may be simpler to use a layer based software like after effect, in the other hand , nodal compositing can be quite effective in other cases, so it's a balance, maybe next time we'll have more luck solving your issues